Optimizing synchronization in multiplex networks of phase oscillators

We present an analytical scheme to achieve optimal synchronization in multiplex networks of frustrated and non-frustrated phase oscillators. We derive a multiplex synchrony alignment function (MSAF) for that purpose, the expression of which consists of structural as well as dynamical information of the layers of the multiplex network. Analyzing the MSAF, a set of frequencies (optimal frequencies) is determined to achieve optimal synchronization in the network. Further, using the scheme, we show that perfect synchronization can be achieved in a layer of the multiplex network for given coupling strength and phase frustration parameters. The analytical scheme presented here has been tested for heterogeneous multiplex networks of frustrated and non-frustrated Kuramoto dynamics.